Hillary Rodham Clinton’s backers in Congress put on a brave face Wednesday as their Democratic presidential candidate continued her stunning slide in the polls, but some of them acknowledged worry spreading through the ranks.

Mrs. Clinton has launched an effort to repair her image that has been damaged by the email scandal dogging her campaign. But a new poll showed liberal rival Sen. Bernard Sanders had edged past her to take a slim lead in Iowa. That put Mr. Sanders ahead in the first two nominating contests: Iowa and New Hampshire.

She said she’s concerned that regardless of how the email controversy plays out — whether with criminal charges or a finding of no wrongdoing — Mrs. Clinton’s foes will be able to label her actions as “reckless.”

The controversy surrounding Mrs. Clinton’s exclusive use of a private email account for official business as secretary of state, and her clumsy handling of questions about it, has contributed to her tumble in the polls.

As Mrs. Clinton struggled to change the subject, the scandal grew to include scrutiny of her handling of classified material and a federal probe that conceivably could lead to criminal charges.

Her likability numbers have taken a big hit, with more and more Americans saying they view her unfavorably, and a majority of voters saying they don’t trust her. The distrust has seeped deep into the party’s base, infecting minorities and women voters who are key to Mrs. Clinton’s strategy.

“The whole email thing is just — I hate to say this — ruining any credibility she had with us working-class mothers,” said Ericka Alston, the business development director for Penn North Community Resource Center, a nonprofit program in one of Baltimore’s poorest and most violent neighborhoods. “The email thing is really dampening how people see her.”

Rep. Charles B. Rangel, New York Democrat and longtime Clinton booster, said there was “no question” that the email scandal had hurt her.

“Opinions by most Americas are not about issues but [if] you like the person. That’s what she’s working on. I know she’s trying,” he said, shaking his head. “I know she’s trying.”

Mr. Rangel knows firsthand about surviving political scandal. In 2010 he was convicted in a House trial of 11 ethics violation and censured, the highest punishment for a congressman short of expulsion.

But Mr. Rangel, 85, rebounded and twice won reelection in his Harlem district.

He said that he didn’t have any advice for Mrs. Clinton, who he said would have to find her own way out of the tangle.

“I don’t know what it is when you have to apologize for something you say you didn’t do. And, quite frankly, if no one says she broke the law, and people keep asking the same questions — it’s a problem,” said Mr. Rangel.

Mrs. Clinton reversed course this week, stopped refusing to apologize and said she was “sorry” for the email setup she used as secretary of state.